TY - JOUR
T1 - Scaling hypothesis leading to generalized extended self-similarity in turbulence
AU - Fujisaka, Hirokazu
AU - Nakayama, Yasuya
AU - Watanabe, Takeshi
AU - Grossmann, Siegfried
PY - 2002/4
Y1 - 2002/4
N2 - A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale r̂, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences ur and for the coarse-grained energy-dissipation rate fluctuations εr, compatible with this GESS, are proposed. The probability density for εr is shown to have the form P r(ε)∼ε-1(r̂/L) sr̂(zr̂(ε)) with zr̂(ε)=ln(ε/ εL)/ln(L/r̂), where L and εL are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function Sr̂(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra Sr̂(z).
AB - A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale r̂, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences ur and for the coarse-grained energy-dissipation rate fluctuations εr, compatible with this GESS, are proposed. The probability density for εr is shown to have the form P r(ε)∼ε-1(r̂/L) sr̂(zr̂(ε)) with zr̂(ε)=ln(ε/ εL)/ln(L/r̂), where L and εL are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function Sr̂(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra Sr̂(z).
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U2 - 10.1103/PhysRevE.65.046307
DO - 10.1103/PhysRevE.65.046307
M3 - Article
AN - SCOPUS:45849156028
VL - 65
SP - 046307/1-046307/16
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 4
M1 - 046307
ER -